Existence of groundstates for a class of nonlinear Choquard equations in the plane

Abstract

We prove the existence of a nontrivial groundstate solution for the class of nonlinear Choquard equation $$-\Delta u+u=(I_{\alpha }\ast F(u))F^{\prime }(u)\text{in }{\mathbb{R}}^2,$$ where $I_{\alpha }$ is the Riesz potential of order $\alpha$ on the plane ${\mathbb{R}}^2$ under general nontriviality, growth and subcriticality on the nonlinearity $F\in C^1(\mathbb{R},\mathbb{R})$.

revised version, 16 pages

References in corpus (1)

• A guide to the Choquard equation

Cited by in corpus (5)

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• On a class of singular Hamiltonian Choquard-type elliptic systems with critical exponential growth
• Semirelativistic Choquard equations with singular potentials and general nonlinearities arising from Hartree-Fock theory